Levene's Test and Welch's t-Test

Two rows, one table, and a decision most papers skip

Run an independent-samples t-test in SPSS and the output table “Independent Samples Test” always contains two rows for every comparison, whether the groups’ variances turn out equal or not.¹ To the left of both rows sits Levene’s test for equality of variances, with its own F statistic and significance value. The table is built this way on purpose: Levene’s result is meant to route you to one row or the other before you ever look at the t, the degrees of freedom, or the P value that follow. In practice, the row that gets copied into the manuscript is very often just the first one — “Equal variances assumed” — because it appears first, because the Levene’s column looks like a footnote rather than an instruction, or because the analyst never learned what that column is for in the first place. Nothing in the layout of the table forces the correct read.

What Levene’s test is actually checking

Levene’s test does not ask whether your two groups differ. It asks a narrower, prior question: whether the two groups have the same population variance.¹ Mechanically, it takes each observation’s absolute deviation from its own group’s centre and runs an ordinary F-test on those deviations, which is why the result looks like an ANOVA output rather than a variance ratio.¹ The null hypothesis is that the variances are equal. A Levene’s P value below .05 rejects that null — the variances are significantly different — and is the signal, in SPSS’s table, to read the “Equal variances not assumed” row instead of the first one. A non-significant Levene’s result does not confirm the variances are equal; it simply fails to find evidence that they are not, which matters more than it sounds, especially in the modest sample sizes typical of surgical studies.

What the second row actually changes

The first row, “Equal variances assumed,” is Student’s original t-test: it pools the two groups’ variances into a single combined estimate and uses n₁ + n₂ − 2 degrees of freedom.² The second row, “Equal variances not assumed,” is Welch’s correction: it keeps each group’s variance separate in the standard error calculation and approximates the degrees of freedom with the Welch–Satterthwaite equation, which weights each group by how much its own variance and sample size contribute to the uncertainty.² That is why Welch’s row nearly always shows a decimal degrees-of-freedom value rather than a whole number, and why it is not a rounding artefact but the correction doing exactly what it is supposed to do. When one group is both smaller and more variable than the other — a common pattern when a novel technique is compared against an established one with a larger, more homogeneous historical cohort — the two rows can produce meaningfully different P values from the same data.

Reading the table: a worked example

The following is illustrative, constructed for demonstration and not drawn from a real dataset. Suppose a single-centre study compares operative time between a new approach (n = 18) and a standard approach (n = 42), and the groups differ in both size and spread. Levene’s test returns F = 6.14, P = .015 — variances are significantly unequal, so the second row governs. The pooled-variance row reports t(58) = 2.31, P = .024; the Welch-corrected row reports t(23.7) = 2.05, P = .052. Reporting the first row here would print a significant finding the data do not actually support at the conventional threshold once the unequal variances are accounted for — the exact failure mode this table exists to prevent.

How to run it — SPSS vs StatsPlease

In IBM SPSS Statistics (documentation current to version 32), the path is Analyze ▸ Compare Means ▸ Independent-Samples T Test…. The continuous outcome goes into the “Test Variable(s)” box and the grouping variable into “Grouping Variable,” with the two group codes entered under “Define Groups.” The Options dialog controls the confidence level for the mean difference, which defaults to 95%. SPSS returns Levene’s F and significance value in the same “Independent Samples Test” table as both t-test rows, rather than as a separate procedure — there is no extra box to tick to request it. The common misread is not a wrong click; it is reading straight across the first row out of habit without glancing left at the Levene’s columns first, which is exactly how a pooled-variance result ends up reported when the second row was the correct one.

Upload the dataset (or the relevant columns). StatsPlease’s deterministic engine checks the relevant assumptions — including variance homogeneity — as part of selecting the appropriate test, using fixed, non-LLM algorithms, and states in the report which assumption checks passed, were violated, or were untestable, and which version of the test was used as a result. The same numbers reproduce running the checks by hand in SPSS.

References

1. Levene H. Robust tests for equality of variances. In: Olkin I, ed. Contributions to Probability and Statistics: Essays in Honor of Harold Hotelling. Stanford, CA: Stanford University Press; 1960:278-292.
2. Welch BL. The generalization of “Student’s” problem when several different population variances are involved. Biometrika. 1947;34(1-2):28-35.
3. Ruxton GD. The unequal variance t-test is an underused alternative to Student’s t-test and the Mann–Whitney U test. Behav Ecol. 2006;17(4):688-690.
4. Delacre M, Lakens D, Leys C. Why psychologists should by default use Welch’s t-test instead of Student’s t-test. Int Rev Soc Psychol. 2017;30(1):92-101.